Can I have two different UV unwrappings of the same object?
Yes, it is possible.

In the mesh panel, under UV Maps, press the "+" button. This will create a new UV map with the same coordinates as the existing one.

For Cycles, in the node editor, select Input -> UV Map to use different UV maps for different shader parts.

In Blender Internal, you can select which UV map to use in the texture panels.